Henry Jackson Henry Jackson - 1 month ago 6x
C Question

How does C compute sin() and other math functions?

I've been poring through .NET disassemblies and the GCC source code, but can't seem to find anywhere the actual implementation of

and other math functions... they always seem to be referencing something else.

Can anyone help me find them? I feel like it's unlikely that ALL hardware that C will run on supports trig functions in hardware, so there must be a software algorithm somewhere, right?

Edit: I'm aware of several ways that functions can be calculated, and have written my own routines to compute functions using taylor series for fun. I'm curious about how real, production languages do it, since all of my implementations are always several orders of magnitude slower, even though I think my algorithms are pretty clever (obviously they're not).


In GNU libm, the implementation of sin is system-dependent. Therefore you can find the implementation, for each platform, somewhere in the appropriate subdirectory of sysdeps.

One directory includes an implementation in C, contributed by IBM. Since October 2011, this is the code that actually runs when you call sin() on a typical x86-64 Linux system. It is apparently faster than the fsin assembly instruction. Source code: sysdeps/ieee754/dbl-64/s_sin.c, look for __sin (double x).

This code is very complex. No one software algorithm is as fast as possible and also accurate over the whole range of x values, so the library implements many different algorithms and its first job is to look at x and decide which algorithm to use. In some regions it uses what looks like the familiar Taylor series. Several of the algorithms first compute a quick result, then if that's not accurate enough, discard it and fall back on a slower algorithm.

Older 32-bit versions of GCC/glibc used the fsin instruction, which is surprisingly inaccurate for some inputs. There's a fascinating blog post illustrating this with just 2 lines of code.

fdlibm's implementation of sin in pure C is much simpler than glibc's and is nicely commented. Source code: fdlibm/s_sin.c and fdlibm/k_sin.c